流体静力和非流体静力气候模式解中的极端事件
Extreme events in solutions of hydrostatic and non-hydrostatic climate models
摘要：
本文首先回顾了在数值天气预报和气候模拟中广泛使用的流体静力（HPE）和非流体静力（NPE）原始方程的数学问题。Cao和Titi（2005，2007）通过证明顶部和底部具有Neumann型边界条件的圆柱上粘性HPE解的存在性和唯一性，为这一问题提供了新的动力。相比之下，NPE的解决方案的规律性仍然是一个悬而未决的问题。考虑到这一HPE规律性结果，本文研究的第二个问题是极端事件是否允许在其解中自发出现。例如，这些事件可能包括不涉及深对流的局部强烈锋的突然出现和消失。分析方法被用来表明，粘性HPE，小尺度结构的创建是允许本地在空间和时间上的大小，规模与雷诺数成反比。
英文摘要：
Initially this paper reviews the mathematical issues surrounding the hydrostatic (HPE) and non-hydrostatic (NPE) primitive equations that have been used extensively in numerical weather prediction and climate modelling. Cao and Titi (2005, 2007) have provided a new impetus to this by proving existence and uniqueness of solutions of viscous HPE on a cylinder with Neumann-like boundary conditions on the top and bottom. In contrast, the regularity of solutions of NPE remains an open question. With this HPE regularity result in mind, the second issue examined in this paper is whether extreme events are allowed to arise spontaneously in their solutions. Such events could include, for example, the sudden appearance and disappearance of locally intense fronts that do not involve deep convection. Analytical methods are used to show that for viscous HPE, the creation of small-scale structures is allowed locally in space and time at sizes that scale inversely with the Reynolds number.
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